This study investigated using acceleration of total body center of
mass (COM) as alternative feedback to conventional joint kinematics for
continuously adjusting stimulation to muscles following spinal cord
injury (SCI) to maintain stable standing against perturbations to
postural balance. Neuroprostheses employing functional neuromuscular
stimulation (FNS) have effectively restored basic standing function
following SCI using preprogrammed stimulation to facilitate sit-to-stand
maneuvers and continuous, constant stimulation to maintain upright
posture [1-2]. Because stimulation is applied at constant levels to
maintain standing, the user is required to exert significant upper-limb
(UL) effort on an assistive device (e.g., walker) to stabilize against
postural disturbances. Sustained UL effort compromises the utility of
standing with FNS by limiting reach and manual function and reduces
standing time by expediting the onset of upper-body fatigue.

Standard joint angle feedback has been extensively investigated for
closed-loop control of standing with FNS. It has been implemented in
isolation for individual joints, including the knees [3-4], hips [5-6],
and ankles [7-8]. These studies showed measures of improvement in
disturbance response but effectively constrained the standing system to
single planes of movement. Comprehensive (ankles, knees, hips, and
trunk) three-dimensional control of standing with FNS based on joint
feedback has been investigated in simulation [9]. Although it
significantly reduced UL effort during postural perturbations when
compared with constant, maximal stimulation, this system required tuning
18 separate gain parameters for the proportional-derivative (PD)
feedback from 9 individual joints. This required instrumentation at each
joint under active control, which may be cumbersome and impractical for
routine clinical deployment. Furthermore, in order to effectively
compensate for the delay between stimulus onset and peak muscle force
generation, standard PD joint feedback gains may be undesirably high,
leaving the control system prone to instability.

Acceleration has been previously suggested as an effective means
for assessing balance [10-12] and offers several potential advantages
over joint-based control of standing with FNS. First, it is sensitive to
the inertial effects of rapidly acting perturbations and can respond
before significant changes in standing posture can occur, thereby
providing a more potent initial feedback signal than position-based
control. Acceleration of the system COM provides a representation of
global system dynamics that are critical for standing control [13].
Finally, adequate measurement of COM acceleration may be plausible with
only a few well-placed accelerometers. This is because perturbed
standing can be represented with a minimal number of synergies [14-15]
and nearly 75 percent of body mass is concentrated centrally across the
pelvis, abdomen, and trunk [16].

The primary objective of this study was to develop and evaluate, in
simulation, a feedback control system for FNS standing that uses
gain-modulated COM acceleration inputs to produce optimal muscle
excitation patterns that counter the effects of postural disturbances.
We employed a model-based approach to determine the feasibility and
basic operating characteristics of the controller prior to online
testing with subjects with SCI. The controller con sisted of using
proportional COM acceleration feedback to drive an artificial neural
network (ANN). We trained this ANN on muscle excitation patterns
optimized to produce target changes in COM acceleration from the
neutral, erect standing posture. To validate the optimal
acceleration-excitation synergy represented by the data used to train
the ANN, we collected electromyographic (EMG) data during systematic
perturbation of nondisabled standing subjects. We compared the COM
acceleration directions in which certain muscle groups were most active
following a perturbation from neutral standing across both data sets. We
evaluated controller performance according to the reduction in UL effort
necessary to stabilize the model against disturbances with active
controller modulation of muscle excitation levels compared with the case
of constant excitation levels analogous to clinical stimulation
paradigms.

METHODS

The overall system included two parallel controllers (FNS muscle
control and UL loading) acting on a three-dimensional model of SCI
bipedal standing ("Three-Dimensional Model of Spinal Cord Injury
Stance" section) to maintain an erect, neutral set point position
(Figure 1). We defined the set point as a single reference position that
the control system was designed to maintain. We selected the most erect
posture corresponding to the highest vertical COM position above the
center of the base of support (BOS) as the desired set point for the
model. The FNS control system employed negative feedback of measured COM
acceleration changes, thereby driving an ANN to modulate muscle
excitation levels to counter the effects produced by postural
disturbances. We represented volitional UL loading by
proportional-integral-derivative (PID) control of the shoulder position
("Upper-Limb Controller" section) corresponding to the set
point. The objective of both the FNS and UL control systems was to
resist disturbances imposed on the standing model while in the set point
posture. We evaluated the FNS controller according to the reduction in
shoulder position controller output (i.e., reduction in UL loading)
under various postural disturbances using feedback controller modulation
of the muscle excitation levels compared with the constant muscle
excitation levels described in the "Determining Optimal and Maximal
Sets of Constant Excitation Levels for Baseline Performance"
section.

[FIGURE 1 OMITTED]

In creating the data space that governs FNS controller action, the
model determined instantaneous changes in COM acceleration induced
across the anterior-posterior (AP) and medial-lateral (ML) dimensions by
changes in activation level from the set point stance for each muscle
group available for FNS control. It then formulated optimal patterns of
muscle activation ("Procedure for Creating Optimal Muscle
Activation Data According to Center of Mass Acceleration in
Targets" section) to produce target changes in COM acceleration
about the erect set point position that were feasible subject to
force-generating capabilities of the included muscle groups. This is
similar to the concept of "induced accelerations" introduced
in Zajac and Gordon [17] to determine the net effect of changes in
muscle activation on joint angular accelerations given a particular
system state. We validated this model-based optimization procedure for
coordinating muscle activity according to changes in COM acceleration
using the EMG data collected from nondisabled individuals undergoing
disturbances while standing ("Collection of Electromyographic Data
of Nondisabled Individuals During Perturbed Bipedal Standing"
section). We compared the net (across AP and ML dimensions) COM
acceleration directions along which muscle groups were most active
between the EMG and model-based data ("Comparing Nondisabled
Electromyographic Data Against Optimal Model-Based Data" section).

We applied the optimization procedure for producing optimal changes
in muscle activation in accordance with targeted changes in COM
acceleration from erect stance to create data representing a synergy
used to train the ANN ("Creating Artificial Neural Network for
Functional Electrical Stimulation Control" section). Each
two-dimensional (AP, ML) COM acceleration target represented a single
training point of inputs, and the corresponding optimal excitation
levels represented a single training point of outputs. For the purposes
of ANN training, we assumed muscle activation, the muscle state variable
determining force output level, to be directly proportional to
excitation, the actual control input and analog for FNS stimulation
level, for ANN training. We subsequently addressed excitation-activation
coupling during forward simulations with specified perturbations
("Perturbation Simulations" section) with optimal tuning of
the feedback controller gains ("Tuning Center of Mass Acceleration
Feedback Controller" section) to minimize UL loading in the
presence of activation dynamics [18]. We observed control system
performance during resistance of disturbances under two-arm and one-arm
support conditions and during simulated one-arm- reaching and
manipulation of a weighted object ("Testing Controller
Performance" section). Nataraj et al. originally described the
models for SCI bipedal standing and volitional UL loading, determination
of baseline excitation levels, and test perturbations [9].

Three-Dimensional Model of Spinal Cord Injury Stance

We developed a three-dimensional computer model of human bipedal
stance in SIMM (Software for Interactive Musculoskeletal Modeling,
MusculoGraphics, Inc; Santa Rosa, California), adapted from a previously
described representation of the lower limbs [19] and trunk [20]. This
model consisted of 9 segments (2 feet, 2 thighs, 2 shanks, pelvis-lumbar
component, and head-arm-trunk complex) with 15 anatomical degrees of
freedom (DOFs) representing bilateral motions of ankle plantar flexion
(PF) and dorsiflexion (DF), ankle inversion and eversion, knee flexion
and extension, hip flexion and extension, internal rotation and external
rotation, hip abduction and adduction, and trunk roll-pitch-yaw. We
included passive moment properties caused by SCI at these DOFs [21].
Both feet were in constant contact with the ground, defining a
closed-chain that effectively reduced the number of independent DOFs to
6 [22]. The lower limbs were in series with a single 3-DOF trunk joint
at the lumbrosacral (lumbar 5-sacral 1) region. A total of 58 muscle
elements were defined across the trunk and lower limbs. When
representing SCI standing by FNS, the only muscle groups actively
controlled in the model were consistent with those targeted by the
existing 16-channel implanted FNS systems listed in Table 1 [23]. We
expect that these implanted systems will be used for individuals with
complete thoracic-level SCI for restoring standing balance. We
constrained elements within each muscle group to act synchronously at
the same level of excitation as if coactivated by a single stimulus
output at a common motor point (e.g., femoral nerve innervating vasti).
Excitation is a normalized quantity (0 to 1). We represented muscles as
Hill-type actuators with nonlinear force dynamics that included
excitation-activation coupling and conventional length-tension and
force-velocity properties [18]. We scaled the peak force parameter for
each SCI muscle group from nondisabled values to produce the maximum
isometric joint moments generated by individuals with complete
thoracic-level SCI in response to electrical stimulation [24].

Upper-Limb Controller

"To approximate [UL] loading that a standing neuroprosthesis
user may need to exert on an assistive support to resist postural
perturbations, three-dimensional stabilization forces were applied to
each shoulder position. PID controller output defined the shoulder force
(SF) in each dimension j ([AP, ML], or inferior-superior defined in
globally fixed reference frame) according to input shoulder position
errors (SE) relative to the reference positions at the set point posture
as follows:

"[UL] controller output acted on shoulder position since the
current model does not explicitly include dynamic representations of the
arms, which would still otherwise produce reaction loads at the
shoulders. The three PID gains ([K.sub.P], [K.sub.I], and [K.sub.D])
were determined according to Ziegler-Nichols 2nd method tuning rules
[25] against a 100 N, 200 ms forward test pulse at the thorax COM. The
same PID gains were used for all three dimensions since only a single
Ziegler-Nichols ultimate gain was observed for the single test
perturbation. This test pulse induced a model trunk acceleration of ~2.5
m/[s.sup.2] which is less than that induced by 'middle level'
perturbations [26]. To approximate typical human operator response, 100
ms pure time delays [27] and muscle force activation delays [18] were
applied to the shoulder force outputs. To simulate one-arm support
conditions, as required to functionally reach on the contralateral side,
only support side shoulder position controller forces were active"
[9]. Nataraj et al. reported and discussed the PID gains [9]. The PID
gains produce support loads typically observed in FNS standing systems
[28].

"To provide a comparative standard for controller performance
across a range of sufficient but constant excitation levels for stable
standing, the 'optimal' and 'maximal' muscle
excitations (Table 1) were determined for the desired set point posture
using the optimizer from [Audu et al.] [29]. The 'optimal'
excitation levels represent the minimum constant excitation levels
sufficient to support stable standing, while the 'maximal'
excitation levels represent the largest constant excitation levels
supporting the same posture. The 'optimal' hip (36.2 N-m) and
knee (11.5 N-m) extension moment constraints were selected as those
minimally necessary to support stable erect standing in energy efficient
postures without joint contractures as reported in [Kagaya et al.] [30].
Joint moment constraints at the trunk (20.2 N-m, [extension]) and ankles
(2.9 N-m, PF) were subsequently selected such that the static [UL]
loading was zero when the model shoulder positions were at the set point
position. For comparison to clinically relevant systems applying
supramaximal stimulation, the 'maximal' set of constant
excitations were specified as all muscles fully excited (excitation =
1.0) except the ankle plantarflexors, which were adjusted to 0.262 as
part of the requirement to minimize static [UL] loading at the set
point. The 'maximal' set drove the knees, hips, and trunk
slightly (<5[degrees]) into hyper-extension, i.e., past set point
position defining full extension. Clinically, this is desired and
commonly observed" [9].

We employed a model-based procedure to generate the data used to
train the ANN in the FNS control system. The procedure determined
optimal muscle activation patterns in accordance with specified COM
acceleration targets, expressed in Cartesian coordinates with respect to
a globally fixed reference frame. We performed the procedure twice, each
with a different muscle set. The first muscle set was restricted to the
16 muscle groups with SCI-adjusted force properties targeted for
activation by an implanted neuroprosthesis. We used data from this
muscle set to train the ANN and develop the FNS controller acting to
resist postural disturbances. The second muscle set represented
nondisabled function and included all 58 muscle groups available across
the trunk and lower limbs without SCI force adjustment. We used results
from this muscle set to validate the procedure against EMG data
collected for nondisabled subjects undergoing standing disturbances
("Collection of Electromyographic Data of Nondisabled Individuals
During Perturbed Bipedal Standing" section). Figure 2 depicts the
procedure, which is outlined as follows.

Step 1

Using the model system equations of motion (SD/ FAST, Symbolic
Dynamics, Inc; Mountain View, California), we determined the maximal COM
acceleration ([a.sub.COM]) induced due to the maximal change in muscle
activation for each muscle group (i) with the initial position state at
the set point position and zero initial velocity and acceleration for
all muscle and skeletal states. The maximal change in muscle activation
([DELTA][M.sub.max]) is the full activation level (normalized to equal
1) minus the baseline muscle activation level ([M.sub.base]) used for
steady-state standing maintenance. In the SCI construction, the baseline
activation levels were set equal to the "optimal" con stant
excitation set described in the "Determining Optimal Maximal Sets
of Constant Excitation Levels for Baseline Performance" section.
For the nondisabled case, we assumed that baseline activation of all 58
muscles was 0, since during quiet standing, we observed EMG activity to
be negligibly low [14]. We also assumed that tibialis anterior does not
produce significant accelerations on the system since its isolated FNS
activity produces net ankle DF, resulting in simple lifting of the
anterior foot (i.e., toe-off) at neutral stance. Consequently, we
removed tibialis anterior from the analysis for the SCI case. We
restricted ankle PF activity to soleus force output with other plantar
flexors (medial, lateral gastrocnemius) omitted despite being
potentially accessible to FNS with a single stimulation channel at the
triceps surae.

[FIGURE 2 OMITTED]

All three muscle heads of the triceps surae could be included; in
this case, however, we noted from pilot experimentation that optimal
excitation levels to the ankle PF group were notably smaller compared
with other muscle groups. This directly resulted from a lack of targeted
musculature that could produce strong anterior shifts in COM
acceleration. This includes certain hip and trunk flexors that pitch the
body forward not being stimulated and ankle DF expectedly yielding
toe-off from erect stance. In turn, the relatively strong posterior COM
accelerations that can be induced from erect stance by the entire
triceps surae muscle group were not as effectively balanced. Including
only soleus essentially desensitized the optimal ankle PF actions to
stimulus input, and we observed that this resulted in better overall
standing performance (i.e., reduced UL loading).

Step 2

Using the [a.sub.COM] values for [DELTA][M.sub.max] of individual
muscle groups, we formulated an optimization to determine the optimal
muscle activation solutions to produce a given COM acceleration target
from the set point stance. Given proportionality between changes in
muscle activation forces and the corresponding accelerations induced
upon the system, the linear constraint equations to be satisfied by the
optimizer yielded the desired net system COM acceleration
([ACC.sub.COM]) targets as follows:

where [W.sub.i] = weighting factor. The net system COM acceleration
is defined here by only two components in the AP and ML directions. We
assumed the third dimension of COM acceleration (in the
inferior-superior direction) to be small enough to be omitted, provided
the system does not collapse given sufficient baseline stimulation to
produce basic constraints (e.g., knees do not buckle) typical for
standing [31]. Each component target represents an optimization
constraint equal to the weighted sum of the respective [a.sub.COM] that
can be induced by an individual muscle group from the baseline level.
[W.sub.i] is the normalized (0 to 1) change in activation from baseline
for each muscle group. We only explored positive (i.e., increase)
changes in activation from baseline levels since we assumed the baseline
levels are fundamentally necessary to maintain basic standing with FNS.
This assumption was necessary since this FNS control system is designed
to operate about erect stance. With only COM acceleration feedback to
modulate stimulation levels, some measure of FNS activation is necessary
to maintain the erect set point when no significant accelerations (e.g.,
quiet standing) are present. Furthermore, without position feedback to
produce alternate combinations of activation that can still preserve the
basic erect standing configuration, we only considered increases from
baseline activations since decreases may overtly compromise the erect
configuration about which these COM acceleration targets are being
defined.

Using the Optimization Toolbox in MATLAB (MathWorks; Natick,
Massachusetts), we determined the solution vectors (W) within the
maximum feasible space of COM acceleration targets. The maximum feasible
target for each direction was simply the sum of the absolute values of
the respective direction of aCOM (listed in Table 2), multiplied by two
(given the symmetry of the left and right side muscle groups). These
maximum feasible values were 2.10, 0.48, and 1.74 m/[s.sup.2] in the
posterior, anterior, and lateral directions, respectively. In creating a
solution space encompassing these limits, COM acceleration targets were
specified between [+ or -] 1.8 m/[s.sup.2] in the ML direction and
between 2.2 and 0.5 m/[s.sup.2] in the AP direction at increments of 0.1
m/[s.sup.2], yielding a total of 1,036 targets. We optimized the
solution vectors (W) according to minimization of an objective criterion
developed for locomotion [32]:

Optimization parameters included a maximum of 10,000 iterations,
constraint equation tolerance of 0.01 m/[s.sub.2] and function tolerance
of 0.001 [N.sup.2]/[m.sup.4]. If the optimizer produced a solution that
met the tolerance for both constraint equations for a given
[ACC.sub.COM], then we classified that COM acceleration target solution
as "feasible." We only retained feasible solution points for
subsequent EMG analysis or ANN training. The two components of
[ACC.sub.COM] served as the inputs and the corresponding 16 absolute
muscle activation solutions ([M.sub.i]) served as the outputs for ANN
training.

To validate the general procedure used to create the muscle
activation synergy from the "Procedure for Creating Optimal Muscle
Activation Data According to Center of Mass Acceleration Targets"
section, we calculated the direction of the resultant COM acceleration
for which activity was highest for different muscle groups for the
model-based synergy and compared it with a similar metric based on the
EMG data collected from three nondisabled volunteers undergoing
systematic external perturbations while standing. None showed nor
reported a history of orthopedic or vestibular problems. We applied
perturbations using software developed in LabVIEW (National Instruments
Corporation; Austin, Texas) to control electromagnetic linear actuators
(STA2506, Copley Controls; Canton, Massachusetts) mounted on customized
framing (80/20 Inc; Columbia City, Indiana) rigidly fixed to either
floor or wall surfaces. Subjects stood with arms crossed and wore a
weight belt approximately at COM level. We positioned it perpendicularly
to four actuator complexes placed in front, back, right, and left of the
subject. We tied four ropes off on one end onto the belt with each rope
connected and directly aligned with the piston of an actuator on the
other end. We used a customized aluminum plate with attached rope cleat
to quickly fasten, adjust for length, and release the rope from the
actuator. All programmed disturbances were discrete force pulses, 250 ms
in duration. We determined the force pulse amplitude threshold that
elicited stepping for each subject in each of the four directions by
trial and error. Perturbations were limited to 80 percent of the
stepping threshold. COM acceleration under these conditions was not a
controlled variable but assumed to be close to the maximal values
possible during stable bipedal standing and could be interpreted as
proportion ally equal in each direction. We applied 30 perturbations on
each subject in each direction.

We recorded EMG signals bilaterally from muscles approximately
coincident with those targeted for stimulation in neuroprosthesis
recipients: tibialis anterior, soleus, vasti, semimembranosus, gluteus
maximus, gluteus medius, adductor magnus, and lower erector spinae. We
collected EMG data using disposable, self-adhesive surface electrodes
placed according to SENIAM (surface EMG for noninvasive assessment of
muscles) standards (http://www.seniam.org). We acquired data with a
Telemyo 900 (Noraxon; Scottsdale, Arizona) at a sampling frequency of
1,500 Hz. EMG signals were rectified and band-limited by a 50 Hz
fourth-order low-pass Butterworth filter offline as specified by
Krishnamoorthy et al. [15]. We determined the mean amplitude (amp) of
the processed EMG during the perturbation period across all trials for
each muscle (j) in each direction (k). For each muscle, we calculated
the EMG activation vector ([??]), representing which net direction is
most active, as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)

where [D.sub.k] = a unit-direction vector in the opposite direction
of the perturbation and is represented in xy-Cartesian coordinates where
[+ or -]x correspond to front and back and [+ or -]y correspond to right
and left. We used the opposite direction of the pull since we assumed
that muscle activity initially increases to resist COM acceleration
effects produced by the disturbances. Final activation vectors were
unity-normalized for graphical display since we only used net
directional information to compare between model and EMG results.

Using standard conversion of Cartesian to polar coordinates, we
calculated the angular coordinate ([[theta].sub.EMG]) of ([??]) for each
muscle to specify the primary direction of activation for each muscle
group opposing the systematic perturbations during nondisabled bipedal
standing. The polar angular coordinate ([[theta].sub.SYN]) serves as the
primary direction of activation for each muscle group according to the
model-based synergy, which we determined from the following activation
vector quantity:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (6)

where [X.sub.j] = the corresponding muscle excitation solution from
the "Procedure for Creating Optimal Muscle Activation Data
According to Center of Mass Acceleration Targets" section. We
observed correspondence between the angular coordinates for the EMG and
model-based vectors for each muscle group.

AP and ML components of each feasible COM acceleration target
resulting from the simulations were the inputs and the corresponding 16
optimal muscle excitation levels were the outputs for a single ANN data
point. We randomly assigned feasible data points for training (70%),
testing (20%), and validating (10%) the ANN. We constructed the ANN with
the Neural Network Toolbox in MATLAB. We employed a three-layer (input,
hidden, output layers) feedforward ANN structure for its universal
mapping capability of nonlinear functions [33]. We determined the number
of hidden layer neurons to be 18 by heuristically finding the number of
neurons providing the lowest mean squared error after 1,000 training
epochs. We normalized all input and output data over [-1, +1] prior to
training. The training function was the Levenberg-Marquardt algorithm
[34]. A maximum of 10,000 epochs were specified for training in lieu of
an early stopping criterion specified as 250 consecutive epochs of
increasing fitting error to the validation set. We calculated the ANN
output sensitivity as the slope for ANN output excitation in each
acceleration direction for each muscle group at neutral stance with zero
acceleration input.

Perturbation Simulations

"In all, 978 perturbation simulations were conducted to
optimally tune and evaluate the controller with respect to total [UL]
loading. Total [UL] loading was the sum of the 'net' force
applied at the left and right shoulders. For each simulation, the
computer model started at the desired erect set point, and [UL] loading
was tracked during the perturbation and following recovery period (750
ms). This recovery period was sufficient to sustain effective
stabilization, defined as [UL] loading within 1% body weight (BW) of its
final steady-state value, across all simulations. Each perturbation
simulation included a single pulse force disturbance applied at a single
location. The location, direction, magnitude, and duration of the
perturbation were varied with each simulation. Perturbations were
applied at the COM locations of the thorax, pelvis, femur, or shank
segment in the forward, backward, left, or right directions relative to
a globally fixed Cartesian reference frame. These force disturbances
ranged from 5% to 15% BW in magnitude and 50 to 500 ms in duration.
Perturbations were also repeated at the system COM, also expressed in
global three-dimensional coordinates" [9].

Tuning Center of Mass Acceleration Feedback Controller

For dynamic controller action, we multiplied each of the two
acceleration inputs (i) to the ANN by its respective proportional gain
([K.sub.P,i]) as follows:

ANN_[Input.sub.i] - [K.sub.P,i] x [ACC.sub.COM-i]. (7)

Gains were optimized to minimize the objective function criterion
of the total two-arm UL loading necessary for stabilization during
perturbation and recovery over all 978 simulations. The gains for both
acceleration inputs were optimally tuned using an asynchronous parallel
pattern set global search algorithm implemented in the APPSPACK [35]
software package running on a FUSION A8 multi-processor computer
(Western Scientific, Inc; Valencia, California). We determined algorithm
parameters such that solutions were found within 100 h of computational
time. These parameters include initial step size equal to 1, step
tolerance equal to 0.01, and step contraction factor equal to 0.985. The
gains were bounded between 0 and -10. The negative value indicates
negative feedback whereby the control system acted to produce effects
that counter the COM acceleration observed during perturbation and
recovery. The initial gain values were based on manual tuning. This
process involved stepwise increments of each feedback gain to minimize
UL loading while holding the other feedback gain to 0. The test
perturbation for manual tuning was a 100 N, 200 ms force pulse at the
thorax.

Testing Controller Performance

External Force Pulse Perturbations

We repeated all 978 perturbation simulations with the feedback
controller active and with constant baseline (optimal or maximal)
excitation levels under two-arm and one-arm support conditions. We
optimally tuned control systems according to two-arm support but tested
them under both support conditions to observe general controller
performance capabilities, including disturbance rejection, while
potentially keeping one arm free for object manipulation. The
fundamental synergy defined by the optimal acceleration-excitation data
remains unchanged regardless of support condition. Even the net synergy
after determination of optimally tuned feedback gains remains symmetric
since only one feedback gain is present for each test dimension.
Furthermore, we expected that with tuning of a similar FNS control
system deployed under live conditions, the subject with SCI would
initially resist external perturbations under two-arm support prior to
testing with one-arm support while performing functional tasks.
Therefore, we found it reasonable to tune under two-arm support
conditions and test for both two-arm and one-arm support in simulation.
We determined the level of significance of any reduction in UL loading
with the controller active compared with baseline across perturbation
direction, location, and magnitude by multiple analysis of variance.

Functional Task Performance

"Functional implications of the controller were assessed in
simulation with application of sinusoidal force loads at one shoulder to
mimic postural disturbances due to weighted, voluntary single arm
movements. Three-dimensional, sinusoidal force loading was applied at
the left shoulder while [UL] control was applied only at the right
shoulder (i.e., one-arm support). The applied sinusoid forces were as
follows: [AP]: 1 Hz, 10 N amplitude, 0 N offset; Right/Left: 1 Hz, 20 N
amplitude, 0 N offset; Superior/Inferior: 0.5 Hz, 20 N amplitude, -50 N
offset. These amplitude and frequency specifications were consistent
with those observed in loaded (2.27 kg) single arm voluntary movements
described in [Triolo et al.] [36]" [9].

RESULTS

Induced Center of Mass Acceleration Results

Table 2 lists the maximum COM acceleration induced from neutral
stance by each SCI muscle group targeted for stimulation. The soleus and
gluteus medius produced the largest induced COM accelerations in the
posterior direction. This is explained by basic anatomical constraints
of the ankles and hips being located below the COM, whereby ankle PF and
hip extension in the sagittal plane would drive the system backward.
Gluteus medius and adductor magnus induced the largest COM accelerations
in the ML dimension. This is also anatomically consistent given their
primary articulations of hip abduction and adduction, whose effects were
largest in the coronal plane. Gluteus maximus and tibialis anterior
produced no changes in COM acceleration since gluteus maximus was
already maximally activated at its initial level and tibialis anterior
was assumed to produce toe-off at erect stance. Only semimembranosus and
erector spinae induced COM accelerations in the anterior direction.
While these muscles extend the hip and trunk, respectively, they both
generate forward motion of the pelvis and lower torso. Anatomical
constraints explain this with semimembranosus producing knee flexion in
conjunction with hip extension and the erector spinae spanning the
entire mid-tolower torso. Prolonged activity of these extensor muscles
may drive the system posteriorly, but their instantaneous effects from
quiet, neutral standing is to shift the COM anteriorly. Vasti and
erector spinae effects were small, relative to other muscles. The vasti
were nearly maximally activated at baseline, and erector spinae did not
produce a very significant instantaneous acceleration at neutral
standing.

Electromyographic Validation of Center of Mass Acceleration Mapping

Figure 3 shows the primary activation directions for each right
side muscle group from both the nondisabled EMG data set and the
nondisabled model synergy. The methodology for EMG collection and
analysis was robust because the standard deviation (SD) about the mean
[[theta].sub.EMG] for all muscle groups was <20[degrees], indicating
that [+ or -]2 SD are encompassed within a single quadrant of the
two-dimensional direction space. The model polar angular coordinate
([[theta].sub.SYN]) was within the quadrant centered about
[[theta].sub.EMG] for all muscle groups except vasti, semimembranosus,
and gluteus maximus. These exceptions in [[theta].sub.EMG] can be
attributed to the positional stabilization required to prevent collapse
during perturbations applied at the lower torso in the live-subject
experiments. Specifically, the increases in EMG activity for
semimembranosus and vasti were likely necessary to prevent hip and knee
flexion induced by forward and backward disturbances, respectively.
Higher gluteus maximus EMG against backward disturbances may be
explained by a co-contraction response in conjunction with antagonist
muscles to generally stiffen the hips. For the other five muscle groups,
good correspondence in activation directions indicate that their
first-response contributions to stabilize standing can be described in
accordance with the initial COM acceleration direction induced by a
perturbation from quiet bipedal standing.

Artificial Neural Network Results

The ANN was capable of accurately outputting the synergistic muscle
excitation patterns optimized according to COM acceleration input
targets. The mean errors (Table 3) in outputs by the ANN for all
feasible COM acceleration target inputs were <0.001. This
demonstrates that the ANN was an effective structure to represent the
synergy that is to be driven by feedback control in forward simulations.
Figure 4 shows the ANN excitation surface outputs for five right-side
muscle groups. Note that tibialis anterior was omitted because of
potential toe-off, and gluteus maximus and vasti were nearly maximally
activated simply to meet the specified optimal baseline requirements for
standing. The output surfaces indicate that the soleus is prominent in
accelerating the system COM backward across the entire feasible target
space. The right semimembranosus has observable increased activity in
accelerating the COM forward. The muscle groups most active in driving
the system COM in the right and left directions were the right adductor
magnus and right gluteus medius, respectively. This follows anatomical
intuition with the ANN providing smooth output of the optimization space
used for ANN training. Sensitivity results in Table 3 suggest that all
targeted muscle groups in Figure 4, except erector spinae, would be
recruited immediately in disturbance rejection as they undergo notable
recruitment to even small (near zero-acceleration point) changes in
acceleration. Erector spinae would be additionally recruited only with
sufficiently increased AP and ML acceleration.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

Controller Gain Tuning

The final feedback gains that minimized total UL loading during
external perturbations were -5.17e-2 and -0.99 for the AP and ML COM
acceleration component inputs, respectively. The higher allowable
feedback gain for the ML component can be explained by greater inherent
stability of bipedal standing in that direction. The BOS is wider in the
ML direction and the standing system approximates a 4-bar linkage [37]
as compared with a more unstable inverted pendulum in the AP direction
[38].

Controller Performance

Figure 5 shows typical two-arm UL loading and muscle-induced joint
moments for baseline and controlleractive conditions. In response to 15
percent BW, 250 ms force pulses applied at the model COM in the AP and
lateral directions, the controller reduced total UL loading during the
perturbation and recovery periods by 43 and 66 percent, respectively.
The controller provided robust return to the set point posture with near
zero final UL loading. The joint moments produced by the controller
during steady-state before and after the perturbation were lower than
maximal baseline as expected and identical to optimal baseline as
designed. The robust return to optimal baseline performance indicates
that acceleration feedback control was transient because the controller
did not produce instabilities requiring excessive UL loading. The peak
UL loading produced with controller action was below that with maximum
baseline stimulation in both perturbation directions.

Consistent with anatomical function, ankle PF and hip extension
were prominent in resisting a forward disturbance. Correspondingly,
right hip abduction and left hip adduction were strongly activated to
reject the rightward disturbance. Trunk extension was small even against
a forward disturbance since it was applied at the system COM, which is
too low to produce significant trunk flexion. Knee extension moments
were small in all cases despite high vasti excitation because the knees
were generally held in hyperextension where length-tension properties
limited force output. The largest (>5 N-m) controller-mediated
changes in joint moments occurred at the ankles and hips, reflecting the
well-described ankle and hip strategies for stable standing [14].

[FIGURE 5 OMITTED]

We observed smooth UL loading and joint moment profiles with
controller feedback despite some oscillations (Figure 5(b)) in the COM
acceleration feedback signal, indicating that the mass-inertia of the
system and delays in muscle force actuation were able to sufficiently
dampen those effects. For a sideward perturbation, ML acceleration was
more prominent as expected, but the AP acceleration component was still
notable. This further underscores how sensitive the SCI standing system
is to destabilizing effects in the AP direction compared with the ML
direction.

Table 4 shows composite simulation results for one-arm and two-arm
resistance to perturbations. Maximal constant excitation always resulted
in lower UL loading than optimal, but the acceleration feedback
controller improved performance over baseline case in all listed
condition cases except backward perturbations. This results from only
semimembranosus being available to induce forward COM accelerations from
neutral stance. UL loading also increased as perturbations were applied
to more superiorly located segments. Perturbations applied to lower
segments were more attenuated by muscle and inertial effects before
greater UL stabilization was required. UL loading is significantly
greater (i.e., standing is more unstable) during one-arm support under
optimal or maximal baseline stimulation. Optimal baseline stimulation
was further ineffective in one-arm support because the model COM
occasionally failed to return to within 0.1 m of its original position.
With the ANN controller active, similar UL loading was expended in
resisting perturbations with either one-arm (21 N) or two-arm (20 N)
support, demonstrating the consistency and value of feedback control.
The mean reduction in UL loading with the controller active compared
with maximal baseline across all force pulse perturbations over both
one-arm and two-arm conditions was 43 percent. The controller produced a
statistically significant reduction in UL loading with rejection of the
null hypothesis of equal means at p = 0.05 across all perturbation
variables (direction, location, amplitude) compared with baseline.
During one-arm functional task performance (FTP), the controller kept
the model erect and reduced UL loading by 51 percent compared with
maximal baseline excitation.

DISCUSSION

To address inherent drawbacks to joint feedback, we proposed and
evaluated the feasibility of COM acceleration feedback for control of
FNS standing. Using a three-dimensional model of bipedal SCI standing,
we developed a control system using COM acceleration feedback to
modulate muscle excitation levels and reduce the UL loading required to
stabilize against postural disturbances. Use of COM acceleration as a
feedback signal follows directly from previous studies that have
implicated acceleration [10-12] and COM dynamics [13] in standing
balance control. In this study, we demonstrated that COM acceleration is
a potentially valuable feedback parameter for characterizing standing
control specifically against perturbations.

We outlined a methodology to produce an optimal synergy that
relates changes in muscle activation from neutral standing to changes in
COM acceleration using our anatomically realistic model. We validated
the resultant synergy by comparing which net direction certain muscle
groups were most active to accelerate the system COM in opposing a
disturbance for a nondisabled model synergy against EMG measurements
recorded from the same muscle groups during systematic perturbation of
nondisabled standing subjects. Five muscle groups (tibialis anterior,
soleus, gluteus medius, adductor magnus, and lower erector spinae)
demonstrated high correspondence between the model-constructed synergy
and live EMG data. This indicates that these muscle groups should be
consistently targeted for FNS control under COM acceleration feedback to
stabilize against disturbances.

However, the remaining three muscle groups (gluteus maximus, vasti,
and semimembranosus) did not correspond well. We postulated that
activity of these muscle groups was modulated according to positional
requirements for maintaining erect stance that are not considered in the
construction of the activation-acceleration map. Thus, it may be best to
reserve these muscle groups for position-based feedback or simply
constant activation for basic standing support. In fact, these same
muscle groups had relatively high baseline activation levels determined
as optimal for sufficiently stable SCI standing (Table 1) and have also
been commonly targeted for stimulation to provide basic standing support
during clinical application [1]. For FNS control of standing that
utilizes feedback of only COM acceleration, position-based corrections
would need to be made volitionally by the user but assisted dynamically
by modulation of stimulation levels for the muscles not reserved for
basic standing support such that user effort was minimized.

For forward simulations of FNS feedback control, we employed the
same activation-acceleration mapping procedure to construct another
model-based synergy using only muscle groups targeted by a 16-channel
implant [23] and reflecting typical FNS force-generating capabilities
following SCI [24]. In simulation, this SCI-specific synergy was
represented by an ANN driven by proportional COM acceleration feedback,
which was more than capable of effectively mapping this synergy between
only two COM acceleration inputs and 16 muscle excitation outputs. With
a prediction error <1e-3 for all outputs, the ANN was successfully
driven by proportional feedback to modulate excitation levels for
reducing UL loading required to resist disturbances compared with the
typical clinical case of maximal constant muscle excitation. COM
acceleration feedback control markedly reduced UL loading across all
external disturbances for both two-arm and one-arm support conditions by
43 percent and during FTP by 51 percent. Disturbance rejection during
one-arm support and FTP are conditions more pertinent to standing
activities of daily living. Thus, future investigations may include
optimizing the control system with one-arm support. However, results
from this study demonstrate similar total UL loading with the controller
active regardless of support condition, suggesting the robustness of
controller action despite the nature of support.

The previous paragraph demonstrates the potential of COM
acceleration feedback to provide a notable improvement in
neuroprosthetic standing performance despite the limited number of
paralyzed muscles available. The same muscles were required to both
support the body against collapse and generate the additional moments
required to reject perturbations. While basic upright support was
achieved with optimal baseline stimulation levels generating necessary
joint moments as reported by Kagaya et al. [30], gluteus maximus and
vasti were nearly maximally activated to produce the necessary baseline
hip and knee extension moments and could not be recruited to resist
disturbances. We also omitted tibialis anterior from the study. Yet
recruitment of the remaining 10 muscles was still sufficient to produce
an effective balance control system in simulation, further highlighting
the potential benefits of COM acceleration feedback.

The formulation of the controller presented in this study is based
on proportional feedback driving an ANN that imposed a synergy to
generate optimal changes in muscle activation to produce desired changes
in COM acceleration and counter effects of postural disturbance about
neutral, erect stance. We employed negative feedback to recruit the
muscles required to oppose the COM accelerations encountered during
perturbation and recovery. We validated this construction by observing
reductions in upper-body loading with simulated one-arm and two-arm
support during a wide range of disturbance locations, amplitudes, and
directions, as well as during simulated functional tasks with our
SCI-adjusted model. Furthermore, our nondisabled EMG data corroborated
this approach and coincided with simulation results indicating that
muscle groups are largely activated to counter the disturbances
reflected in COM acceleration direction. We consistently observed
model-predicted COM accelerations to be in the opposite direction of the
net action of the most active muscles during repeated disturbances.
Notable exceptions (vasti and gluteus maximus) can be attributed
primarily to muscle recruitment for other objectives, such as the
necessary positional corrections to prevent frank system failure and
outright falls. This underlies the notion that comprehensive standing is
a complex, multi-sensory task [39] that employs joint-based feedback.
Theoretically, some form of position or joint-based control would be
required to replicate the intact balance control apparatus and achieve
truly hands-free standing with FNS. However, coordination of muscle
activity according to COM acceleration still seems to characterize much
of the initial standing response to applied disturbances. More
importantly, this synergy may be exploited for substantially extending
and improving the functionality of standing neuroprostheses.

This approach for constructing a muscle-based acceleration synergy
for neuroprosthetic standing was inspired by Kuo and Zajac [31], who
developed an algorithm to generate feasible acceleration sets (FAS)
composed of joint angular accelerations for all feasible normalized
muscle activations subject to observed experimental constraints (e.g.,
knees-locked, heel and toe lift-off) of sagittal plane standing. That
study used the FAS to identify which muscles, if strengthened, would
produce the greatest increases in standing mobility. Our study created
feasible, optimal activation patterns that could generate targeted
changes in linear COM acceleration, the proposed sensor-based feedback
variable for control of SCI standing.

Although this article supports the use of COM acceleration as a
potentially effective feedback variable controlling standing with FNS,
additional work is still required to implement such a control system
clinically. The clinical viability of acceleration-based feedback
control depends on performance in the presence of typical sources of
feedback error (e.g., sensor placement, measurement accuracy, soft
tissue effects). The model system presented serves as an appropriate
test-bed for future studies to systematically introduce feedback error
and quantify its effects on performance. Most importantly, efficient
techniques need to be developed to fit, tune, and specify system
parameters for a particular user in a clinical setting. Methods have
been previously outlined for determining user-specific musculoskeletal
and UL controller parameters to develop a model-based system for initial
controller tuning and evaluation prior to laboratory implementation [9].
While this study employed a generic bipedal model of standing to
conceptually validate the proposed control system producing a
potentially substantial improvement in standing performance, creation of
user-specific models would be necessary to develop model-based solutions
for control systems for specific users. This would include scaling the
muscle geometry, muscle force-generating capabilities, and length and
mass-inertia properties of segments. Only an accurate description of
those features would generate an optimal control solution that produces
kinematic and kinetic responses in simulation that appropriately
represent those expected to be observed during live laboratory
performance.

The methods from Nataraj et al. for creating user-specific control
systems were suggested for a joint feedback system composed of PD inputs
from nine individual joints [9]. Properly assessing performance to
robustly tune a system with that many feedback gains during live
conditions may be intractable. Both model and laboratory development of
FNS control systems can be expedited with control structures containing
fewer feedback variables. The control system examined in this article
employs only two feedback variables (AP and ML COM acceleration) that
would need to be measured and two feedback gains that would need to be
tuned.

While a user-specific model-based solution could still be explored,
a paradigm could also be devised to produce the data (Equations (2) and
(3)) used to construct the optimal synergy entirely from a live user.
The subject with paralysis could be at neutral erect stance in a walker
while sufficient but minimal constant stimulation is applied as the
"baseline activation." Stimulation could then be discretely
ramped from baseline levels for individual muscles ([W.sub.i]) and the
corresponding peak induced COM acceleration ([a.sub.COM,i]) could be
recorded. This peak would serve only as an estimate of the [a.sub.COM,i]
induced by a particular muscle group since it would occur across the
excitation-activation coupling dynamics, and small postural changes away
from the neutral set point position may occur. However, the extent to
which the assumption of linear superposition governing Equations (2) and
(3) breaks down should be investigated experimentally. Given that
significant changes in acceleration can occur without large changes in
configuration, the suggested methodology could realistically produce a
viable solution for neuroprosthetic standing. Finally, an instrumented
walker employing load-sensitive handles could be used to tune the system
online against disturbances applied by the perturbation system described
in the "Collection of Electromyographic Data of Nondisabled
Individuals During Perturbed Bipedal Standing" section, as well as
provide a metric of goodness of fit for a clinical system.

CONCLUSIONS

COM acceleration may be an advantageous alternative to joint
kinematics as a feedback variable for control of FNS standing. This
study suggests that even with control of only 16 SCI-paralyzed muscles
available to provide basic standing support, significant improvement in
disturbance rejection can still be achieved with COM acceleration
feedback modulation of muscle excitation levels. Further study to
demonstrate potential clinical viability is necessary, such as
evaluating performance robustness in the presence of expected feedback
measurement errors. Ultimately, control systems should be developed
according to user-specific characteristics for laboratory testing with
live subjects with SCI.

Over 25% of individuals with spinal cord injury (SCI) are veterans,
and functional neuromuscular stimulation (FNS) has been proven effective
in restoring basic mobility following paralysis. This article
investigates a novel feedback controller for improving balance function
following SCI using an implantable FNS standing system. The controller
was developed and tested using a computer model of the human legs and
trunk. Inclusion of feedback control improved balance function by 43% in
the model. Future work will concentrate on customizing this control
system for specific users and testing under live laboratory conditions.

Financial Disclosures: The authors have declared that no competing
interests exist.

Funding/Support: This material was based on work supported by the
National Institutes of Health (grant R01 NS040547-04A2) and the Motion
Study Laboratory, Louis Stokes Cleveland Department of Veterans Affairs
Medical Center.

Participant Follow-up: The authors do not plan to inform
participants of the publication of this study. However, participants
have been encouraged to contact the laboratory regarding status of the
study and related publications.